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An Introduction to Measure-Theoretic Probability. Edition No. 2
Description:
An Introduction to Measure-Theoretic Probability, Second Edition, employs a classical approach to teaching
students of statistics, mathematics, engineering, econometrics, finance, and other disciplines that measure
theoretic probability. This book requires no prior knowledge of measure theory, discusses all its topics in
great detail, and includes one chapter on the basics of ergodic theory and one chapter on two cases of
statistical estimation. There is a considerable bend toward the way probability is actually used in statistical
research, finance, and other academic and nonacademic applied pursuits. This book provides in a concise,
yet detailed way, the bulk of the probabilistic tools that a student working toward an advanced degree in
statistics, probability and other related areas should be equipped with.
- Provides in a concise, yet detailed way, the bulk of probabilistic tools essential to a student working toward
an advanced degree in statistics, probability, and other related fields
- Includes extensive exercises and practical examples to make complex ideas of advanced probability
accessible to graduate students in statistics, probability, and related fields
- All proofs presented in full detail and complete and detailed solutions to all exercises are available to the
instructors on book companion site
Considerable bend toward the way probability is used in statistics in non-mathematical settings in academic,
research and corporate/finance pursuits.
Contents:
Preface
1. Certain Classes of Sets, Measurability, Pointwise Approximation
2. Definition and Construction of a Measure and Its Basic Properties
3. Some Modes of Convergence of a Sequence of Random Variables and Their Relationships
4. The Integral of a Random Variable and Its Basic Properties
5. Standard Convergence Theorems, The Fubini Theorem
6. Standard Moment and Probability Inequalities, Convergence in the r-th Mean and Its Implications
7. The Hahn-Jordan Decomposition Theorem, The Lebesgue Decomposition Theorem, and The RadonNikcodym Theorem
8. Distribution Functions and Their Basic Properties, Helly-Bray Type Results
9. Conditional Expectation and Conditional Probability, and Related Properties and Results
10. Independence
11. Topics from the Theory of Characteristic Functions
12. The Central Limit Problem: The Centered Case
13. The Central Limit Problem: The Noncentered Case
14. Topics from Sequences of Independent Random Variables
15. Topics from Ergodic Theory
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